Acronym tutcupa toe (alt.: tutaltut toetric)
Name tuta atop toe,
(tut,inv tut,toe)-trigonic
Circumradius sqrt(21/8) = 1.620185
Lace city
in approx. ASCII-art 
  x3x3o      
             
             
o3x3x   x3x3x
Face vector 48, 144, 162, 81, 17
Confer
uniform relative:
sirhin  
segmentotera:
deca aprip  
general polytopal classes:
segmentotera   lace simplices  

This polyteron occurs as wedge within sirhin. In fact it is a segment of deca aprip, which in turn is a segment of sirhin.


Incidence matrix according to Dynkin symbol

oxx3xxx3xox&#x   → height(1,2) = 1/sqrt(2) = 0.707107
                   height(1,3) = height(2,3) = sqrt(5/8) = 0.790569

o..3o..3o..    | 12  *  * |  2 1  2  2 0  0  0  0  0  0 | 1 2  1  2  2  2  1  2  2 0 0  0  0  0 0 0 0 | 1 1 1 2  1  2  2 1 1 2 0 0 0 0 0 | 1 1 1 2 1 0
.o.3.o.3.o.    |  * 12  * |  0 0  2  0 1  2  2  0  0  0 | 0 0  2  2  1  2  0  0  0 2 1  2  2  1 0 0 0 | 0 2 1 1  2  2  1 0 0 0 1 2 1 1 0 | 1 2 1 1 0 1
..o3..o3..o    |  *  * 24 |  0 0  0  1 0  0  1  1  1  1 | 0 0  0  0  0  1  1  1  1 0 0  1  1  1 1 1 1 | 0 0 0 0  1  1  1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
... x.. ...    |  2  0  0 | 12 *  *  * *  *  *  *  *  * | 1 1  0  1  0  0  0  1  0 0 0  0  0  0 0 0 0 | 1 1 0 1  0  1  0 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0
... ... x..    |  2  0  0 |  * 6  *  * *  *  *  *  *  * | 0 2  0  0  2  0  0  0  2 0 0  0  0  0 0 0 0 | 1 0 1 2  0  0  2 0 1 2 0 0 0 0 0 | 1 0 1 2 1 0
oo.3oo.3oo.&#x |  1  1  0 |  * * 24  * *  *  *  *  *  * | 0 0  1  1  1  1  0  0  0 0 0  0  0  0 0 0 0 | 0 1 1 1  1  1  1 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0
o.o3o.o3o.o&#x |  1  0  1 |  * *  * 24 *  *  *  *  *  * | 0 0  0  0  0  1  1  1  1 0 0  0  0  0 0 0 0 | 0 0 0 0  1  1  1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    |  0  2  0 |  * *  *  * 6  *  *  *  *  * | 0 0  2  0  0  0  0  0  0 2 0  2  0  0 0 0 0 | 0 2 1 0  2  0  0 0 0 0 1 2 1 0 0 | 1 2 1 0 0 1
... .x. ...    |  0  2  0 |  * *  *  * * 12  *  *  *  * | 0 0  0  1  0  0  0  0  0 1 1  0  1  0 0 0 0 | 0 1 0 1  0  1  0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
.oo3.oo3.oo&#x |  0  1  1 |  * *  *  * *  * 24  *  *  * | 0 0  0  0  0  1  0  0  0 0 0  1  1  1 0 0 0 | 0 0 0 0  1  1  1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    |  0  0  2 |  * *  *  * *  *  * 12  *  * | 0 0  0  0  0  0  1  0  0 0 0  1  0  0 1 1 0 | 0 0 0 0  1  0  0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
... ..x ...    |  0  0  2 |  * *  *  * *  *  *  * 12  * | 0 0  0  0  0  0  0  1  0 0 0  0  1  0 1 0 1 | 0 0 0 0  0  1  0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
... ... ..x    |  0  0  2 |  * *  *  * *  *  *  *  * 12 | 0 0  0  0  0  0  0  0  1 0 0  0  0  1 0 1 1 | 0 0 0 0  0  0  1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
o..3x.. ...    |  3  0  0 |  3 0  0  0 0  0  0  0  0  0 | 4 *  *  *  *  *  *  *  * * *  *  *  * * * * | 1 1 0 0  0  0  0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
... x..3x..    |  6  0  0 |  3 3  0  0 0  0  0  0  0  0 | * 4  *  *  *  *  *  *  * * *  *  *  * * * * | 1 0 0 1  0  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
ox. ... ...&#x |  1  2  0 |  0 0  2  0 1  0  0  0  0  0 | * * 12  *  *  *  *  *  * * *  *  *  * * * * | 0 1 1 0  1  0  0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... xx. ...&#x |  2  2  0 |  1 0  2  0 0  1  0  0  0  0 | * *  * 12  *  *  *  *  * * *  *  *  * * * * | 0 1 0 1  0  1  0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... xo.&#x |  2  1  0 |  0 1  2  0 0  0  0  0  0  0 | * *  *  * 12  *  *  *  * * *  *  *  * * * * | 0 0 1 1  0  0  1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo3ooo3ooo&#x |  1  1  1 |  0 0  1  1 0  0  1  0  0  0 | * *  *  *  * 24  *  *  * * *  *  *  * * * * | 0 0 0 0  1  1  1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x |  1  0  2 |  0 0  0  2 0  0  0  1  0  0 | * *  *  *  *  * 12  *  * * *  *  *  * * * * | 0 0 0 0  1  0  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... x.x ...&#x |  2  0  2 |  1 0  0  2 0  0  0  0  1  0 | * *  *  *  *  *  * 12  * * *  *  *  * * * * | 0 0 0 0  0  1  0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.x&#x |  2  0  2 |  0 1  0  2 0  0  0  0  0  1 | * *  *  *  *  *  *  * 12 * *  *  *  * * * * | 0 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x.3.x. ...    |  0  6  0 |  0 0  0  0 3  3  0  0  0  0 | * *  *  *  *  *  *  *  * 4 *  *  *  * * * * | 0 1 0 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
... .x.3.o.    |  0  3  0 |  0 0  0  0 0  3  0  0  0  0 | * *  *  *  *  *  *  *  * * 4  *  *  * * * * | 0 0 0 1  0  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x |  0  2  2 |  0 0  0  0 1  0  2  1  0  0 | * *  *  *  *  *  *  *  * * * 12  *  * * * * | 0 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .xx ...&#x |  0  2  2 |  0 0  0  0 0  1  2  0  1  0 | * *  *  *  *  *  *  *  * * *  * 12  * * * * | 0 0 0 0  0  1  0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .ox&#x |  0  1  2 |  0 0  0  0 0  0  2  0  0  1 | * *  *  *  *  *  *  *  * * *  *  * 12 * * * | 0 0 0 0  0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..x ...    |  0  0  6 |  0 0  0  0 0  0  0  3  3  0 | * *  *  *  *  *  *  *  * * *  *  *  * 4 * * | 0 0 0 0  0  0  0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..x ... ..x    |  0  0  4 |  0 0  0  0 0  0  0  2  0  2 | * *  *  *  *  *  *  *  * * *  *  *  * * 6 * | 0 0 0 0  0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..x3..x    |  0  0  6 |  0 0  0  0 0  0  0  0  3  3 | * *  *  *  *  *  *  *  * * *  *  *  * * * 4 | 0 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
o..3x..3x..    ♦ 12  0  0 | 12 6  0  0 0  0  0  0  0  0 | 4 4  0  0  0  0  0  0  0 0 0  0  0  0 0 0 0 | 1 * * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
ox.3xx. ...&#x ♦  3  6  0 |  3 0  6  0 3  3  0  0  0  0 | 1 0  3  3  0  0  0  0  0 1 0  0  0  0 0 0 0 | * 4 * *  *  *  * * * * * * * * * | 1 1 0 0 0 0
ox. ... xo.&#x ♦  2  2  0 |  0 1  4  0 1  0  0  0  0  0 | 0 0  2  0  2  0  0  0  0 0 0  0  0  0 0 0 0 | * * 6 *  *  *  * * * * * * * * * | 1 0 1 0 0 0
... xx.3xo.&#x ♦  6  3  0 |  3 3  6  0 0  3  0  0  0  0 | 0 1  0  3  3  0  0  0  0 0 1  0  0  0 0 0 0 | * * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦  1  2  2 |  0 0  2  2 1  0  2  1  0  0 | 0 0  1  0  0  2  1  0  0 0 0  1  0  0 0 0 0 | * * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... xxx ...&#x ♦  2  2  2 |  1 0  2  2 0  1  2  0  1  0 | 0 0  0  1  0  2  0  1  0 0 0  0  1  0 0 0 0 | * * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... xox&#x ♦  2  1  2 |  0 1  2  2 0  0  2  0  0  1 | 0 0  0  0  1  2  0  0  1 0 0  0  0  1 0 0 0 | * * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3x.x ...&#x ♦  3  0  6 |  3 0  0  6 0  0  0  3  3  0 | 1 0  0  0  0  0  3  3  0 0 0  0  0  0 1 0 0 | * * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x ♦  2  0  4 |  0 1  0  4 0  0  0  2  0  2 | 0 0  0  0  0  0  2  0  2 0 0  0  0  0 0 1 0 | * * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... x.x3x.x&#x ♦  6  0  6 |  3 3  0  6 0  0  0  0  3  3 | 0 1  0  0  0  0  0  3  3 0 0  0  0  0 0 0 1 | * * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.x.3.x.3.o.    ♦  0 12  0 |  0 0  0  0 6 12  0  0  0  0 | 0 0  0  0  0  0  0  0  0 4 4  0  0  0 0 0 0 | * * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.xx3.xx ...&#x ♦  0  6  6 |  0 0  0  0 3  3  6  3  3  0 | 0 0  0  0  0  0  0  0  0 1 0  3  3  0 1 0 0 | * * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.xx ... .ox&#x ♦  0  2  4 |  0 0  0  0 1  0  4  2  0  2 | 0 0  0  0  0  0  0  0  0 0 0  2  0  2 0 1 0 | * * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .xx3.ox&#x ♦  0  3  6 |  0 0  0  0 0  3  6  0  3  3 | 0 0  0  0  0  0  0  0  0 0 1  0  3  3 0 0 1 | * * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..x3..x    ♦  0  0 24 |  0 0  0  0 0  0  0 12 12 12 | 0 0  0  0  0  0  0  0  0 0 0  0  0  0 4 6 4 | * * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
ox.3xx.3xo.&#x ♦ 12 12  0 | 12 6 24  0 6 12  0  0  0  0 | 4 4 12 12 12  0  0  0  0 4 4  0  0  0 0 0 0 | 1 4 6 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oxx3xxx ...&#x ♦  3  6  6 |  3 0  6  6 3  3  6  3  3  0 | 1 0  3  3  0  6  3  3  0 1 0  3  3  0 1 0 0 | 0 1 0 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oxx ... xox&#x ♦  2  2  4 |  0 1  4  4 1  0  4  2  0  2 | 0 0  2  0  2  4  2  0  2 0 0  2  0  2 0 1 0 | 0 0 1 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... xxx3xox&#x ♦  6  3  6 |  3 3  6  6 0  3  6  0  3  3 | 0 1  0  3  3  6  0  3  3 0 1  0  3  3 0 0 1 | 0 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3x.x3x.x&#x ♦ 12  0 24 | 12 6  0 24 0  0  0 12 12 12 | 4 4  0  0  0  0 12 12 12 0 0  0  0  0 4 6 4 | 1 0 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.xx3.xx3.ox&#x ♦  0 12 24 |  0 0  0  0 6 12 24 12 12 12 | 0 0  0  0  0  0  0  0  0 4 4 12 12 12 4 6 4 | 0 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1

or
(tuta || toe)   → height(12,3) = 1/sqrt(2) = 0.707107

o..3o..3o..    & | 24  * |  2  1  2  2  0  0 | 1 2  3  2  2  1  2  2 0 0 | 1 3 1  3  2 1  1 2 0 | 1 3 1 1
..o3..o3..o      |  * 24 |  0  0  0  2  2  1 | 0 0  0  0  1  2  2  2 2 1 | 0 0 0  2  1 2  2 2 1 | 0 2 1 2
-----------------+-------+-------------------+---------------------------+----------------------+--------
... x.. ...    & |  2  0 | 24  *  *  *  *  * | 1 1  0  1  0  0  1  0 0 0 | 1 2 0  0  1 1  0 1 0 | 1 2 0 1
... ... x..    & |  2  0 |  * 12  *  *  *  * | 0 2  2  0  0  0  0  2 0 0 | 1 2 1  2  0 0  1 2 0 | 1 2 1 1
oo.3oo.3oo.&#x   |  2  0 |  *  * 24  *  *  * | 0 0  2  1  1  0  0  0 0 0 | 0 2 1  2  1 0  0 0 0 | 1 2 1 0
o.o3o.o3o.o&#x & |  1  1 |  *  *  * 48  *  * | 0 0  0  0  1  1  1  1 0 0 | 0 0 0  2  1 1  1 1 0 | 0 2 1 1
..x ... ...    & |  0  2 |  *  *  *  * 24  * | 0 0  0  0  0  1  0  1 1 1 | 0 0 0  1  0 1  2 1 1 | 0 1 1 2
... ..x ...      |  0  2 |  *  *  *  *  * 12 | 0 0  0  0  0  0  2  0 2 0 | 0 0 0  0  1 2  0 2 1 | 0 2 0 2
-----------------+-------+-------------------+---------------------------+----------------------+--------
o..3x.. ...    & |  3  0 |  3  0  0  0  0  0 | 8 *  *  *  *  *  *  * * * | 1 1 0  0  0 1  0 0 0 | 1 1 0 1
... x..3x..    & |  6  0 |  3  3  0  0  0  0 | * 8  *  *  *  *  *  * * * | 1 1 0  0  0 0  0 1 0 | 1 1 0 1
ox. ... ...&#x & |  3  0 |  0  1  2  0  0  0 | * * 24  *  *  *  *  * * * | 0 1 1  1  0 0  0 0 0 | 1 1 1 0
... xx. ...&#x   |  4  0 |  2  0  2  0  0  0 | * *  * 12  *  *  *  * * * | 0 2 0  0  1 0  0 0 0 | 1 2 0 0
ooo3ooo3ooo&#x   |  2  1 |  0  0  1  2  0  0 | * *  *  * 24  *  *  * * * | 0 0 0  2  1 0  0 0 0 | 0 2 1 0
o.x ... ...&#x & |  1  2 |  0  0  0  2  1  0 | * *  *  *  * 24  *  * * * | 0 0 0  1  0 1  1 0 0 | 0 1 1 1
... x.x ...&#x & |  2  2 |  1  0  0  2  0  1 | * *  *  *  *  * 24  * * * | 0 0 0  0  1 1  0 1 0 | 0 2 0 1
... ... x.x&#x & |  2  2 |  0  1  0  2  1  0 | * *  *  *  *  *  * 24 * * | 0 0 0  1  0 0  1 1 0 | 0 1 1 1
..x3..x ...    & |  0  6 |  0  0  0  0  3  3 | * *  *  *  *  *  *  * 8 * | 0 0 0  0  0 1  0 1 1 | 0 1 0 2
..x ... ..x      |  0  4 |  0  0  0  0  4  0 | * *  *  *  *  *  *  * * 6 | 0 0 0  0  0 0  2 0 1 | 0 0 1 2
-----------------+-------+-------------------+---------------------------+----------------------+--------
o..3x..3x..    & ♦ 12  0 | 12  6  0  0  0  0 | 4 4  0  0  0  0  0  0 0 0 | 2 * *  *  * *  * * * | 1 0 0 1
ox.3xx. ...&#x & ♦  9  0 |  6  3  6  0  0  0 | 1 1  3  3  0  0  0  0 0 0 | * 8 *  *  * *  * * * | 1 1 0 0
ox. ... xo.&#x   ♦  4  0 |  0  2  4  0  0  0 | 0 0  4  0  0  0  0  0 0 0 | * * 6  *  * *  * * * | 1 0 1 0
oxx ... ...&#x & ♦  3  2 |  0  1  2  4  1  0 | 0 0  1  0  2  1  0  1 0 0 | * * * 24  * *  * * * | 0 1 1 0
... xxx ...&#x   ♦  4  2 |  2  0  2  4  0  1 | 0 0  0  1  2  0  2  0 0 0 | * * *  * 12 *  * * * | 0 2 0 0
o.x3x.x ...&#x & ♦  3  6 |  3  0  0  6  3  3 | 1 0  0  0  0  3  3  0 1 0 | * * *  *  * 8  * * * | 0 1 0 1
o.x ... x.x&#x & ♦  2  4 |  0  1  0  4  4  0 | 0 0  0  0  0  2  0  2 0 1 | * * *  *  * * 12 * * | 0 0 1 1
... x.x3x.x&#x & ♦  6  6 |  3  3  0  6  3  3 | 0 1  0  0  0  0  3  3 1 0 | * * *  *  * *  * 8 * | 0 1 0 1
..x3..x3..x      ♦  0 24 |  0  0  0  0 24 12 | 0 0  0  0  0  0  0  0 8 6 | * * *  *  * *  * * 1 | 0 0 0 2
-----------------+-------+-------------------+---------------------------+----------------------+--------
ox.3xx.3xo.&#x   ♦ 24  0 | 24 12 24  0  0  0 | 8 8 24 12  0  0  0  0 0 0 | 2 8 6  0  0 0  0 0 0 | 1 * * *
oxx3xxx ...&#x & ♦  9  6 |  6  3  6 12  3  3 | 1 1  3  3  6  3  6  3 1 0 | 0 1 0  3  3 1  0 1 0 | * 8 * *
oxx ... xox&#x   ♦  4  4 |  0  2  4  8  4  0 | 0 0  4  0  4  4  0  4 0 1 | 0 0 1  4  0 0  2 0 0 | * * 6 *
o.x3x.x3x.x&#x & ♦ 12 24 | 12  6  0 24 24 12 | 4 4  0  0  0 12 12 12 8 6 | 1 0 0  0  0 4  6 4 1 | * * * 2

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